Nikolaos Karaliolios

activity

20142026

most citedGlobal aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups

12 citations · 47 across the 13 of their papers we have counts for

collaborators

13 papers

math.DS2026

A note on cocycles in $T \times S O (3)$

Nikolaos Karaliolios

This short note studies $C^{\infty}$ -smooth cocycles in $T \times S O (3)$ that have $0$ degree and are non-homotopic to constants. The study picks up from where the author's…

math.DS2024

Furstenberg counterexamples over Diophantine rotations

Nikolaos Karaliolios

We construct cocycles in $T \times S U (2)$ over Diophantine rotations that are minimal and not uniquely ergodic. Such cocycles are dense in an open subset of cocycles over…

math.NA2024

The weak form of the SDOF and MDOF equation of motion, part II: A numerical method for the SDOF problem

Nikolaos Karaliolios, Dimitiros L. Karabalis

A new, more efficient, numerical method for the SDOF problem is presented. Its construction is based on the weak form of the equation of motion, as obtained in part I of the paper,…

math.NA2024

The weak form of the SDOF and MDOF equation of motion, part I: Theory

Nikolaos Karaliolios, Dimitrios L. Karabalis

The weak form of the SDOF and MDOF equations of motion are obtained. The original initial conditions problem is transformed into a boundary value problem. The boundary value proble…

cs.LG2024

Smooth Pseudo-Labeling

Nikolaos Karaliolios, Hervé Le Borgne, Florian Chabot

Semi-Supervised Learning (SSL) seeks to leverage large amounts of non-annotated data along with the smallest amount possible of annotated data in order to achieve the same level of…

math.DS2020★ 2 cited

Anosov-Katok constructions for quasi-periodic $SL (2, R)$ cocycles

Nikolaos Karaliolios, Xu Xu, Qi Zhou

We prove that if the frequency of the quasi-periodic $SL (2, R)$ cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\frac{1…

math.DS2019★ 3 cited

Fibered rotation vector and hypoellipticity for quasiperiodic cocycles in compact Lie groups

Nikolaos Karaliolios

Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi-periodic cocycles in $T^{d} \times G$ , $G$ a compact Lie g…

math.DS2017★ 1 cited

Cohomological rigidity and the Anosov-Katok construction

Nikolaos Karaliolios

We provide a general argument for the failure of Anosov-Katok-like constructions (as in \cite{AFKo2015} and \cite{NKInvDist}) to produce Cohomologically Rigid diffeomorphisms in ma…

math.DS2016★ 11 cited

Local Rigidity of Diophantine translations in higher dimensional tori

Nikolaos Karaliolios

We prove a theorem asserting that, given a Diophantine rotation $α$ in a torus $\T ^{d} \equiv \R ^{d} / \Z ^{d}$, any perturbation, small enough in the $C^{\infty}$ topology, that…

math.DS2015★ 9 cited

Continuous spectrum or measurable reducibility for quasiperiodic cocycles in $T^{d} \times S U (2)$

Nikolaos Karaliolios

We continue our study of the local theory for quasiperiodic cocycles in $T^{d} \times G$ , where $G = S U (2)$ , over a rotation satisfying a Diophantine condition and satisfyi…

math.DS2015★ 12 cited

Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups

Nikolaos Karaliolios

In this mémoire we study quasiperiodic cocycles in semi-simple compact Lie groups. For the greatest part of our study, we will focus ourselves to one-frequency cocyles. We will pro…

math.DS2014★ 8 cited

Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups

Nikolaos Karaliolios

We study close-to-constants quasiperiodic cocycles in $T^{d} \times G$ , where $d \in N^{*}$ and $G$ is a compact Lie group, under the assumption that the rotat…

math.DS2014★ 1 cited

Invariant Distributions and local theory of quasiperiodic cocycles in $T^{d} \times S U (2)$ }

Nikolaos Karaliolios

We study the linear cohomological equation in the smooth category over quasi-periodic cocycles in $T^{d} \times S U (2)$ . We prove that, under a full measure condition on t…

A note on cocycles in T×SO(3)

Furstenberg counterexamples over Diophantine rotations

The weak form of the SDOF and MDOF equation of motion, part II: A numerical method for the SDOF problem

The weak form of the SDOF and MDOF equation of motion, part I: Theory

Smooth Pseudo-Labeling

Anosov-Katok constructions for quasi-periodic SL(2,R) cocycles

Fibered rotation vector and hypoellipticity for quasiperiodic cocycles in compact Lie groups

Cohomological rigidity and the Anosov-Katok construction

Local Rigidity of Diophantine translations in higher dimensional tori

Continuous spectrum or measurable reducibility for quasiperiodic cocycles in Td×SU(2)

Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups

Differentiable Rigidity for quasiperiodic cocycles in compact Lie groups

Invariant Distributions and local theory of quasiperiodic cocycles in Td×SU(2)}

A note on cocycles in $T \times S O (3)$

Anosov-Katok constructions for quasi-periodic $SL (2, R)$ cocycles

Continuous spectrum or measurable reducibility for quasiperiodic cocycles in $T^{d} \times S U (2)$

Invariant Distributions and local theory of quasiperiodic cocycles in $T^{d} \times S U (2)$ }